Class 08 NCERT Chapters

Have you seen graphs in the newspapers, television, magazines, books etc.? The purpose of the graph is to show numerical facts in visual form so that they can be understood quickly, easily and clearly. Thus graphs are visual representations of data collected.

Let us take a natural number, say 30, and write it as a product of other natural numbers, say 30 = 2 × 15 = 3 × 10 = 5 × 6. Thus, 1, 2, 3, 5, 6, 10, 15 and 30 are the factors of 30. Of these, 2, 3 and 5 are the prime factors of 30.

Mohan prepares tea for himself and his sister. He uses 300 mL of water, 2 spoons of sugar, 1 spoon of tea leaves and 50 mL of milk. How much quantity of each item will he need, if he has to make tea for five persons?

Mass of earth is 5,970,000,000,000,000,000,000,000 kg. We have already learnt in earlier class how to write such large numbers more conveniently using exponents, as, 5.97 × 10²⁴ kg.

We have learnt that for a closed plane figure, the perimeter is the distance around its boundary and its area is the region covered by it. We found the area and perimeter of various plane figures such as triangles, rectangles, circles, etc.

In earlier classes, we have already become familiar with what algebraic expressions (or simply expressions) are. Examples of expressions are: x + 3, 2y - 5, 3x² , 4xy + 7

We know, ratio means comparing two quantities. A basket has two types of fruits, say, 20 apples and 5 oranges. Then, the ratio of the number of oranges to the number of apples = 5 : 20. The comparison can be done by using fractions as, 5/20 = 1/4 The number of oranges is 1/4 th the number of apples. In terms of ratio, this is 1 : 4, read as, "1 is to 4"

This is a story about one of India’s great mathematical geniuses, S. Ramanujan. Once another famous mathematician Prof. G.H. Hardy came to visit him in a taxi whose number was 1729.

You know that the area of a square = side × side (where ‘side’ means ‘the length of a side’).

The information collected in all such cases is called data. Data is usually collected in the context of a situation that we want to study.

You know that the paper is a model for a plane surface. When you join a number of points without lifting a pencil from the paper (and without retracing any portion of the drawing other than single points), you get a plane curve.

In the earlier classes, you have come across several algebraic expressions and equations. Some examples of expressions we have so far worked with are: 5x, 2x – 3, 3x + y, 2xy + 5, xyz + x + y + z, x² + 1, y + y²

In Mathematics, we frequently come across simple equations to be solved. For example, the equation x + 2 = 13 is solved when x = 11, because this value of x satisfies the given equation.